**5. Lump-hole theory**

146 Recent Advances in Crystallography

**4. σ-hole theory** 

3). The key to the halogen bonds is the polarizability of the halogen atom. Therefore, the strongest halogen bonds are formed by the most easily polarizable halogens, and the

Halogen bonds are commonly defined as electrostatic interactions between Lewis acids (the halogen atom) and neutral or anionic Lewis bases and abbreviated as XB, where X refers to the halogen and B the Lewis base.[11] The strong directional preferences of a halogen bond arise from the tendency to maximize the main two directional attractive contributions to the interaction energy i.e. electrostatics and charge transfer. These, in turn, minimize the exchange repulsion that is also strongly directional. Optimizing the electrostatic and charge transfer aspects have been successfully used in designing of drugs, liquid crystals, organic semiconductors, magnetic materials, nonlinear optical materials, and templates for solid synthesis.[12–16] Conventionally, halogen bonds have been divided into two classes, TypeI and Type II (Fig. 3), based solely on the bonding geometry.[4] A few theories and concepts have been proposed for rationalizing the XB in greater detail. The most familiar one is the σhole theory. Other theories such as the lump-and-hole theory and the concept of amphoteric

strength of the halogen bonds typically decreases in the order I > Br > Cl > F.

halogen bonds have been used to cover the "blind spots" in the σ-hole theory.

positivity of the σ-hole increases in the order F ‹ Cl ‹ Br ‹ I.

potential (red) on pentafluoroiodobenzene.

In most cases, the σ-hole theory has successfully explained the contradictory nature of halogen bonding. Conventionally covalently bonded halogens are seen as negatively charged entities. How, then, is it possible that they can participate in inter-atomic interactions as electron acceptors? In the σ-hole theory the σ-holes are defined as regions of positive electrostatic potential on the outer sides of halogen atoms, centered close to the extension of the halogen atoms' covalent bonds (Fig.4).[17]In general three factors determine the σ-hole's presence or absence and their magnitudes: a) the polarizability of the halogen atom, b) its electronegativity, and c) the electron-withdrawing power of the remainder D of the D-X molecule.[17] When the halogen is more polarizable and has lower electronegativity, the potential of the σ-hole can become more strongly positive. So the

**Figure 4.** Regions of concentrated negative electrostatic potential (blue) and regions of depleted

The σ-Hole theory has satisfactorily explained most halogen bonding interactions, but it fails in some cases. For example, CH3Cl can form a halogen bond with OCH2, which is impossible according to the σ-hole theory because of the lack of a positive potential region around the Cl.[17,18] In lump-hole theory there are no true positive regions of the halogen bond donor. The charge density is, however, polarized and there are regions of charge depletion and charge concentration on the donor and acceptor. When these two interact, the areas with charge concentration on the halogen bond acceptors are interacting with the charge depleted areas of the halogen bond donor. Based on lump-hole theory, the participation of fluorine in halogen bonds can be also explained, since a true positive σ-hole is not needed.
